Improvement of wave height forecast in deep and intermediate waters with the use of stochastic methods Zoe Theocharis, Constantine Memos, Demetris Koutsoyiannis National Technical University of Athens School of Civil Engineering WISE 6, Venice Presentation Structure. Introduction. Methodology. Applications. Conclusions WISE 6, Venice
Introduction WISE 6, Venice Introduction OBJECTIVE: : Improvement of the forecast power of numerical wave models using real time measurements Improvement of wave predictions can be achieved by three different approaches: Data assimilation techniques (require re-run run and space coverage) Stochastic tools Neural networks techniques WISE 6, Venice
Only a few stochastic applications concerning real time improvement of the wave forecast Caires & Sterl,, : non parametric correction of ERA- reanalysis data, using a learning dataset In this work a stochastic technique is applied to measured data of wave height for improving forecasts of the wave model WISE 6, Venice 5 Methodology WISE 6, Venice 6
Bivariate Linear Regression models Yˆ t + k t = ak X t + k t + t β ky + γ κ Yˆ : Y : Χ : Wave height estimate Wave height measurement Wave height model forecast k=,, < model,, > Trivariate linear model < model > WISE 6, Venice 7 Bivariate Non-Linear Regression models Y λ t+ t = α Χ λ t+ t + β Y λ t + γ, if Y t c, Y λ t+ t = α Χ λ t+ t + β Yλ t + γ, if Y t c γ = γ + (β - β ) c λ (continuity c) <model > WISE 6, Venice 8
Applications WISE 6, Venice 9 First Application: The Aegean Sea The Stations Used WISE 6, Venice
very irregular coastline complicated bottom topography presence of a large number of islands scattered over the area abrupt changes in magnitude and direction of the wind field WISE 6, Venice Underestimation Mean Wave ΜΕΣΟΙ Height ΟΡΟΙ Measurement- ΥΨΟΥΣ ΚΥΜΑΤΟΣ (m) Forecast.6...8.6.. Measurements through POSEIDON System 5 6 7 8 9 ΜΗΝΕΣ -hour months time step Measur ΜΕΣΟΙ ΟΡΟΙ ΜΕΤΡΗΣΕΙΣ Measurement ΜΕΣΟΙ ΟΡΟΙ WISE 6, Venice ATHOS STATION
Underestimation Measurements through POSEIDON System Wave ΥΨΟΣ Height ΚΥΜΑΤΟΣ Measurement- ΜΕΤΡΗΣΕΙΣ- forecast (m) 7 6 5 5 67 89 5 67 89 5 67 89 5 67 89 5 67 89 55 55 555 5657 5859 66 66 665 6667 6869 77 77 -hour time step ΧΡΟΝΙΚΑ months ΒΗΜΑΤΑ ΩΡΩΝ ΜΕΤΡΗΣΗ Measur ΠΡΟΒΛΕΨΗ Measurement WISE 6, Venice ATHOS STATION Μodel.5 --Measurement ΜΕΤΡΗΣΗ -- Forecast ΜΟΝΤΕΛΟ 6. ΜΟΝΤΕΛΟ --Model.5.5.5 7 6 9 5 8 7 6 9 5 55 58 6 6 67 7 7 76 79 8 85 88 9 9 97 ΥΨΟΣ Wave ΚΥΜΑΤΟΣ Height (m) (m) -hour time step ΧΡΟΝΙΚΑ ΒΗΜΑΤΑ ΩΡΩΝ WISE 6, Venice ATHOS STATION
7 Wave ΥΨΟΣ Height ΚΥΜΑΤΟΣ (m) (m) 6 5 Approximation of the measured average wave height Significant decrease of the standard deviation --Measurement ΜΕΤΡΗΣΗ -- Forecast ΜΟΝΤΕΛΟ 6. --Model 77 5 9 5 8 57 5 69 685 76 87 9 989 65 7 9 69 5 5 597 67 79 85 9 977 5 9 5 8 57 WISE 6, Venice 5.5 ΥΨΟΣ ΚΥΜΑΤΟΣ-.5.5.5 y =.68x +.999 R =.78 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ Wave 6..Α (m) Height Forecast (m).5 5 6 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ 5.5.5.5.5.5 y =.99x +.67 R =.979 Wave Height Measurement (m) 5 6 9.6 N 9. N 9. N 9 N 8.8 N ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m) Wave Height Measurement (m) 5.5 E 6 E 6.5 E WISE 6, Venice 6 Dardan Ocean Data View m 5m 5m m m
5.5 ΥΨΟΣ ΚΥΜΑΤΟΣ- (m) ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ 6..Α Wave (m) Height Forecast (m).5.5.5.5 y =.5x +.96 R =.79 5 7.7 N 6 6 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m) 5 y =.99x +. R =.957 7.6 N 7.5 N 7. N 7. N 7. N 5 E 5. E 5. E 5.6 E Ocean Data View 5 5 5 6 WISE 6, Venice 7 ΥΨΟΣ ΚΥΜΑΤΟΣ ΜΕΤΡΗΣΗ (m) Wave Height Measurement (m) ΥΨΟΣ ΚΥΜΑΤΟΣ- (m) ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΟΝΤΕΛΟ (6.) Wave (m) Height Forecast (m).5.5.5.5 y =.556x +.88 R =.677.5.5.5.5.5.5 ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΗ (m).5.5.5.5 y =.975x +.88 R =.975 6.6 N 6.5 N 6. N 6. N m 5m 5m m.5.5.5.5.5 6. N WISE 6, Venice ΥΨΟΣ ΚΥΜΑΤΟΣ-ΜΕΤΡΗΣΕΙΣ (m) 5. E 5. E 5. E 5. E 5.5 E 5.6 E8 Wave Height Measurement (m) Ocean Data View
Summary Table R Athos R Lesvos R Mykonos R Santorini MODEL.78.7.7.676 MODEL.9.89.97.96 MODEL.865.8.86.8 MODEL.9.895.9.9 MODEL a.99.897.96.99 MODEL b.99.898.95.98 WISE 6, Venice 9 Total improvement οbtained: For all four stations For all four models tested For all periods of implementation For high and low values of the wave height No outliers Increase of the forecast time step decreases the predictive accuracy of our technique Our technique s s R^ equals s for forecasts horizon more than days WISE 6, Venice
nd application: Indian Ocean Two stations: one in deep waters (station ) One in intermediate waters (station ) Distance: 9Km cycle WISE 6, Venice WAVE ΥΨΟΣ ΚΥΜΑΤΟΣ. HEIGHT ΜΕΤΡΗΣΕΙΣ ΚΑΙ measurement- ΜΟΝΤΕΛΟ, ANOIXTA ΙΝ ΙΚΗΣ ΧΕΡΣΟΝΗΣΟΥ (station ),5 WAVE HEIGHT ΥΨΟΣ ΚΥΜΑΤΟΣ,5,5,5 overestimation,5 5 6 7 8 9 5 6 7 8 9 5 6 7 8 9 No Assim Buoy Active Swell Subroutine WAVE HEIGHT ΥΨΟΣ ΚΥΜΑΤΟΣ,,8,6,,,,8,6 ΥΨΟΣ ΚΥΜΑΤΟΣ. ΜΕΤΡΗΣΕΙΣ ΚΑΙ ΜΟΝΤΕΛΟ, ΠΑΡΑΚΤΙΑ ΙΝ ΙΚΗΣ ΧΕΡΣΟΝΗΣΟΥ WAVE HEIGHT measurement- (station ) Outliers for two days both in deep and intermediate waters,,, 5 56 67 78 89 55 66 77 88 99 5 65 76 87 98 9 WISE 6, Venice No Assim Buoy
ΕΦ ΑΡΜΟΓΗ Non linear ΣΤΟΧΑΣΤΙΚΟΥ stochastic model ΜΟΝΤΕΛΟΥ to improve ΑΠΟ station ΒΑΘΕΙΑ ΣΕ ΡΗΧΑ ΝΕΡΑ. ΙΝ ΙΚΟΣ ΩΚΕΑΝΟΣ. ΠΡΟΓΝΩΣΗ ΣΤΟ +9 wave height forecast using station data ΥΨΟΣ Wave ΚΥΜΑΤΟΣ height,5,5,5,5,5 ΜΕΤΡΗΣΗ MEASUREMENT NON LINEAR REGRESSION 9 58 77 96 5 5 7 9 9 8 67 86 Remarkable improvement Coefficient of determination (R^=.9) Approximation of the measured average wave height Absorbing the outliers K time step selection WISE 6, Venice Conclusions WISE 6, Venice
All models improve significantly the forecast in applications tested The parameters (weights) in all models indicate the same performance in all stations and in all periods of implementation The relation between measurements and predictions seems to be the same (error source, systematic error) If we have/measure the wave height for a small period of - months irrespectively of the season, we can:. Estimate the variable weights and then. Significantly improve in real time the forecast of the wave model without re-running running it and within an area of considerable extent containing the point of measurement Stochastic models are a useful tool for wave forecast. Future research is needed WISE 6, Venice 5